Chapter 2.4, Problem 39E

To determine

To show:that there is a number csuch that $f\left(c\right)=1000$ .

Answer to Problem 39E

the $f\left(x\right)$ function is continuous everywhere.

Explanation of Solution

Given:

  $f\left(x\right)=x^2+10\sin x$ .

Calculation:

Consider the given function is $f\left(x\right)=x^2+10\sin x$ .

Now,

  $f\left(0\right)=0^2+10\sin 0=0$

  $\underset{x\to \infty }{\lim }f\left(x\right)=x^2+10\sin x=\infty$

Hence, the $f\left(x\right)$ function is continuous everywhere.